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We present a method to compute the intrinsic spin Hall conductivity fromfirst principles using an interpolation scheme based on maximally-localizedWannier functions. After obtaining the relevant matrix elements among the abinitio Bloch states calculated on a coarse k-point mesh, we Fourier transformthem to find the corresponding matrix elements between Wannier states. We thenperform an inverse Fourier transform to interpolate the velocity andspin-current matrix elements onto a dense k-point mesh, and use them toevaluate the spin Hall conductivity as a Brillouin-zone integral. This strategyhas a much lower computational cost than a direct ab initio calculation,without sacrificing the accuracy. We demonstrate that the spin Hallconductivities of platinum and doped gallium arsenide, computed with ourinterpolation scheme as a function of the Fermi energy, are in good agreementwith those obtained in previous first-principles studies. We also discusscertain approximations that can be made, in the spirit of the tight-bindingmethod, to simplify the calculation of the velocity and spin-current matrixelements in the Wannier representation.

Computation of intrinsic spin Hall conductivities from first principles using maximally-localized Wannier functions